Journal of Plasma Physics

Linear and nonlinear resonant interaction of sound waves in dissipative layers

a1 Center for Plasma Astrophysics, KU Leuven, Celestijnenlaan 200B, B-3001 Leuven-Heverlee, Belgium
a2 Space and Atmosphere Research Centre, Department of Applied Mathematics, University of Sheffield, Sheffield S3 7RH, UK

The theory of resonant nonlinear magnetohydrodynamic (MHD) waves in dissipative steady plasmas developed by Ballai and Erdélyi is used to study the effect of steady flows on nonlinear resonant heating of MHD waves in (a) linear, (b) weakly and (c) strongly nonlinear approximations. Nonlinear connection formulae for slow MHD waves are derived. This nonlinear theory of driven MHD waves is then used to study the interaction of sound waves with one-dimensional isotropic steady plasmas. We find that a steady equilibrium flow can significantly influence the efficiency of resonant absorption in the considered limits. In the case of strong nonlinearity, the efficiency of the resonant coupling is found to be proportional to the counterpart obtained in linear theory. The factor of proportion is approximately of the order of unity, justifying the commonly applied linear approximations.

(Received October 25 1999)
(Revised February 4 2000)